One of the problems frequently mentioned as a candidate for quantum advantage is that of selecting a portfolio of financial assets to maximize returns while minimizing risk. In this paper we formulate several real-world constraints for use in a Quantum Annealer (QA), extending the scenarios in which the algorithm can be implemented. Specifically, we show how to add fundamental analysis to the portfolio optimization problem, adding in asset-specific and global constraints based on chosen balance sheet metrics. We also expand on previous work in improving the constraint to enforce investment bands in sectors and limiting the number of assets to invest in, creating a robust and flexible solution amenable to QA. Importantly, we analyze the current state-of-the-art algorithms for solving such a problem using D-Wave's Quantum Processor and compare the quality of the solutions obtained to commercially-available optimization software. We explore a variety of traditional and new constraints that make the problem computationally harder to solve and show that even with these additional constraints, classical algorithms outperform current hybrid solutions in the static portfolio optimization model.
One of the problems frequently mentioned as a candidate for quantum advantage is that of selecting a portfolio of financial assets to maximize returns while minimizing risk. In this paper we formulate several real-world constraints for use in a Quantum Annealer (QA), extending the scenarios in which the algorithm can be implemented. Specifically, we show how to add fundamental analysis to the portfolio optimization problem, adding in asset-specific and global constraints based on chosen balance sheet metrics. We also expand on previous work in improving the constraint to enforce investment bands in sectors and limiting the number of assets to invest in, creating a robust and flexible solution amenable to QA. Importantly, we analyze the current state-of-the-art algorithms for solving such a problem using D-Wave's Quantum Processor and compare the quality of the solutions obtained to commercially-available optimization software. We explore a variety of traditional and new constraints that make the problem computationally harder to solve and show that even with these additional constraints, classical algorithms outperform current hybrid solutions in the static portfolio optimization model.
In this paper we show how to implement in a simple way some complex real-life constraints on the portfolio optimization problem, so that it becomes amenable to quantum optimization algorithms. Specifically, first we explain how to obtain the best investment portfolio with a given target risk. This is important in order to produce portfolios with different risk profiles, as typically offered by financial institutions. Second, we show how to implement individual investment bands, i.e., minimum and maximum possible investments for each asset. This is also important in order to impose diversification and avoid corner solutions. Quite remarkably, we show how to build the constrained cost function as a quadratic binary optimization (QUBO) problem, this being the natural input of quantum annealers. The validity of our implementation is proven by finding the optimal portfolios, using D-Wave Hybrid and its Advantage quantum processor, on portfolios built with all the assets from S&P100 and S&P500. Our results show how practical daily constraints found in quantitative finance can be implemented in a simple way in current NISQ quantum processors, with real data, and under realistic market conditions. In combination with clustering algorithms, our methods would allow to replicate the behaviour of more complex indexes, such as Nasdaq Composite or others, in turn being particularly useful to build and replicate Exchange Traded Funds (ETF).
In this work, we introduce a new workflow to solve portfolio optimization problems on annealing platforms. We combine a classical preprocessing step with a modified unconstrained binary optimization (QUBO) model and evaluate it using simulated annealing (classical computer), digital annealing (Fujitsu’s Digital Annealing Unit), and quantum annealing (D-Wave Advantage). Starting from Markowitz’s theory on portfolio optimization, our classical preprocessing step finds the most promising assets within a set of possible assets to choose from. We then modify existing QUBO models for portfolio optimization, such that there are no limitations on the number of assets that can be invested in. Furthermore, our QUBO model enables an investor to also place an arbitrary amount of money into each asset. We apply this modified QUBO to the set of promising asset candidates we generated previously via classical preprocessing. A solution to our QUBO model contains information about what percentage of the whole available capital should be invested into which asset. For the evaluation, we have used publicly available real-world data sets of stocks of the New York Stock Exchange as well as common ETFs. Finally, we have compared the respective annealing results with randomly generated portfolios by using the return, variance, and diversification of the created portfolios as measures. The results show that our QUBO formulation is capable of creating well-diversified portfolios that respect certain criteria given by an investor, such as maximizing return, minimizing risk, or sticking to a certain budget.
Portfolio optimization (PO) plays a central role in finance, encompassing both resource allocation and risk management. While numerous algorithms have been developed for continuous-variable PO, the inclusion of large, indivisible assets such as real estate transforms the task into a combinatorial optimization problem, which is NP-hard for classical computers. This study explores using quantum-classical hybrid algorithms for multi-discretized portfolio optimization, addressing the needs of real-world applications. We propose a flexible theoretical model that can solve PO problems with various types of discrete assets and constraints, which is compatible with both quantum and classical computing paradigms. Then, we use the D-Wave quantum processor and classical solver to determine optimal investment strategies. Experimental results indicate that the hybrid quantum algorithm outperforms both classical computing methods and quantum annealing algorithms in terms of return and risk management. This research enhances quantum computing applications in finance and provides insights into future algorithm design.
Recent advances in quantum hardware offer new approaches to solve various optimization problems that can be computationally expensive when classical algorithms are employed. We propose a hybrid quantum-classical algorithm to solve a dynamic asset allocation problem where a target return and a target risk metric (expected shortfall) are specified. We propose an iterative algorithm that treats the target return as a constraint in a Markowitz portfolio optimization model, and dynamically adjusts the target return to satisfy the targeted expected shortfall. The Markowitz optimization is formulated as a Quadratic Unconstrained Binary Optimization (QUBO) problem. The use of the expected shortfall risk metric enables the modeling of extreme market events. We compare the results from D-Wave's 2000Q and Advantage quantum annealers using real-world financial data. Both quantum annealers are able to generate portfolios with more than 80% of the return of the classical optimal solutions, while satisfying the expected shortfall. We observe that experiments on assets with higher correlations tend to perform better, which may help to design practical quantum applications in the near term.
Quantum annealing has emerged as a promising computational paradigm for solving large-scale combinatorial optimization problems that are intractable for classical algorithms. Financial portfolio optimization, which involves balancing expected returns against risk under multiple practical constraints, represents one of the most challenging optimization tasks in quantitative finance. Traditional approaches based on mean-variance theory, heuristic meta-optimization, and classical quadratic programming often struggle to scale efficiently as the dimensionality of assets and constraints increases. This study explores the application of quantum annealing techniques to financial portfolio optimization by formulating the problem as a quadratic unconstrained binary optimization model suitable for quantum hardware. The paper provides a systematic mapping of portfolio objectives and constraints into the Ising Hamiltonian framework and analyzes how quantum tunneling and probabilistic state transitions can enhance convergence toward near-global optima. Comparative insights between classical solvers and quantum annealing-based approaches are discussed in terms of solution quality, computational efficiency, and scalability. Furthermore, the study highlights current hardware limitations, embedding challenges, and noise effects that influence optimization performance. The findings indicate that quantum annealing offers substantial potential for accelerating portfolio optimization in high-dimensional financial systems, particularly in scenarios involving complex constraints and dynamic market conditions, thereby establishing a foundation for future quantum-driven financial decision-support systems.
Quantum computing, leveraging principles such as superposition and entanglement, has shown remarkable potential in solving complex optimization problems. Quantum annealing (QA) is particularly effective for combinatorial optimization and has gained increasing attention in financial applications. However, financial decision-making problems typically involve conflicting objectives, such as the trade-off between minimizing risk and maximizing returns, posing challenges for current QA approaches in efficiently encoding multi-objective problems and constraints. To address this gap, we propose the first quantum annealing framework for bi-objective weighted portfolio optimization based on the trend ratio model, integrating D-Wave's latest constrained quadratic model (CQM) hybrid solver. Our approach offers flexibility to accommodate diverse investor preferences. Experimental evaluations using real-world U.S. stock market data demonstrate the effectiveness of our method, showing higher-quality solutions and faster runtimes compared to classical multi-objective optimization algorithms. These promising results highlight the significant potential of quantum computing in practical financial optimization scenarios.